Nuprl Lemma : Game-minus_functionality
∀G1,G2:Game.  (G1 ≡ G2 
⇒ -(G1) ≡ -(G2))
Proof
Definitions occuring in Statement : 
eq-Game: G ≡ H
, 
Game-minus: -(G)
, 
Game: Game
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
eq-Game: G ≡ H
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
Game-minus: -(G)
, 
left-indices: left-indices(g)
, 
right-indices: right-indices(g)
, 
mkGame: {mkGame(f[a] with a:L | g[b] with b:R}
, 
Wsup: Wsup(a;b)
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
guard: {T}
, 
exists: ∃x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
top: Top
, 
right-option: right-option{i:l}(g;m)
, 
left-option: left-option{i:l}(g;m)
, 
or: P ∨ Q
Lemmas referenced : 
Game-induction, 
all_wf, 
Game_wf, 
eq-Game_wf, 
Game-minus_wf, 
left-indices_wf, 
right-indices_wf, 
or_wf, 
left-option_wf, 
right-option_wf, 
subtype_rel_self, 
left_move_minus_lemma, 
right-move_wf, 
equal_wf, 
exists_wf, 
left-move_wf, 
right_move_minus_lemma, 
eq-Game_inversion
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isectElimination, 
thin, 
sqequalRule, 
lambdaEquality, 
instantiate, 
hypothesis, 
cumulativity, 
functionEquality, 
hypothesisEquality, 
independent_functionElimination, 
lambdaFormation, 
independent_pairFormation, 
productElimination, 
dependent_functionElimination, 
dependent_pairFormation, 
applyEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
inrFormation, 
inlFormation, 
because_Cache
Latex:
\mforall{}G1,G2:Game.    (G1  \mequiv{}  G2  {}\mRightarrow{}  -(G1)  \mequiv{}  -(G2))
Date html generated:
2018_05_22-PM-09_53_50
Last ObjectModification:
2018_05_20-PM-10_41_20
Theory : Numbers!and!Games
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